7. Continuous Variables (II)

In this lecture, I’ve briefly reviewed the notion of ``propagators” because of its application (we’d back to this in chapters related to quantum dynamics) and showed that Hilbert space unavoidably contains discontinuous wavefunctions. We’ve actually shown that the Schrodinger equation itself, can evolve a continuous, differentiable, square-integrable function into a discontinuous one! then talked about the notion of ``separability” of a Hilbert space briefly (because quantum mechanics doesn’t have to do anything with this. The relevant difficulties arise when dealing with quantization of fields).